Introduction Welcome Letter 2 2: Fill & Download for Free

Please read this entirely. Let me stop the mayhem that is bound to ensue. This question is just a rehash of 6÷2(2+1). First off, there is NO UNIVERSAL ANSWER. This math problem exploits a small loophole in conventions and principles. I took computer engineering in university which was fully paid for. I topped every mathematics and science class in my high school and first couple years of university. I'm not telling you this to brag, but rather to put in perspective the vast experience I had as a math student. I lived and breathed math. I loved it. It was fun for me, rather than work. Since this problem emerged, I researched it casually for a couple of years and here is my personal take on the matter:→There is no 'right' answer because there are multiple conventions which lead to either answer. However, I would argue that lacking a declaration of the convention used, there is a "more correct" answer than the other, and that would be ONE (1), and here is why. There is more to just the Order of Operations. In any equation of expression, you need to know what the operands are (values, numbers, variables, etc) and how they are represented. In this case, a non-standard notation is used for the expression. You will rarely see anything like this in any college/university text, if at all. And if you do, the author will have clearly let you know what the intentions were to understand it. However ... if you back this up just a little, and use a very COMMON notation, it starts to make sense. What is 8 ÷ 2x ? Clearly by every book (that I have seen) the answer is 4/x and not 4x. In that expression, '2x' is a single operand/value. It is a 'quantity'. That quantity is actually a product of factors. The factors are 2 and x. By the principle of factors, they are interchangeable, and defined as "2 is a factor of 2x, and x is a factor of 2x". This is in line with "coefficients". 2 is a coefficient of x and x is a coefficient of 2. 2x = x2, but we usually write the numerical coefficient first. Therefore, 8 ÷ 2x = 8 ÷ x2. These basic definitions are the basis for Algebra which date back to the 1800's: Intro to Algebra: Bonnycastle, Quantities on pg 13"a and b are factors of ab" "3abc is a composite quantity."pg 25simple quantities, examples on pg 26https://books.google.ca/books/about/Bonnycastle_s_Introduction_to_Algebra.html?id=1YhTAAAAYAAJ&redir_esc=y→You will find counter arguments along the lines of: "But isn't 2x really only 2 * x?" (What they are getting at is 8 ÷ 2x = 8 ÷ 2 * x = (8÷2) * x = 4x ). Yes of course 2x = 2 * x, but if you understand what is 2x in an expression, then you can't change the notation without CORRECTLY doing so. 8 ÷ 2x = 8 ÷ (2 * x), since 2x is a single quantity AND a product of its own factors. Remember, the factors are 2 and x. IF you change the notation to 8 ÷ 2 * x, then what you have illegally done is change the factor 2, to ½ ! Here is how:8 ÷ 2x ; here we have the quantity 2x, factors/coefficients are 2 and x8 ÷ 2 * x ; Here, this is the same as 8/2 * x which equals 8 * ½ * x = 8 * (½)x. The factors 2 and x have now (illegally) become ½ and x without any operations taking place.→Counter counter argument: cos2x . Most people who know trig, know that this is cos(2x) and NOT cos2 * x = [cos(2)] * x. This sort of shows you an example why changing a quantity to its basic form in the middle of an expression requires some understanding of basic principles.→Now, I have also heard the argument: "But the rules for using letters (variables) and actual numbers (digits) are different." Obviously untrue. This is vital to understand. No matter what symbols we use: digits, letters, Greek letters, or any other symbol we want, the rules do not change.→There are also assertions that "Any author may use any convention they want, as long as they state what that convention is at the beginning of the book". This is correct. BUT ... lacking any sort of declaration, we should still revert to some common convention, and, in my opinion, that should be one which nearly every mathematician uses in text books written for and used in universities around the world, for decades, if not HUNDREDS of years.→Here are just a few references I have found from around the world that are online for your reading pleasure. As far as I know, most don't have some "declaration of convention" stated anywhere, and still use the product of factors rule (single quantity).Introduction to Real Analysis by Bartle and Sherberthttp://iuuk.mff.cuni.cz/~andrew/bartle_introduction-to-real-analysis-new-edition.pdfpage 42: (x²-2)/2xpage 53: 1/2n = 1/(2n)pg 350: e/2Mpg 363: 1/n(n+1) < 1/n² <= 1/n and n/(n-2)(n-1)Measure and Integral: An Introduction to Real Analysis By Richard Wheeden, Antoni Zygmund 1977https://www.scribd.com/doc/275407108/Richard-Wheeden-Antoni-Zygmund-Measure-and-Integral-Pure-and-Applied-Mathematics-1977on page 31: 2Mε/4(k + 1)M = ε/2(k + 1)Introduction to Real Analysis: William F. Trenchhttp://ramanujan.math.trinity.edu/wtrench/texts/TRENCH_REAL_ANALYSIS.PDFpg 123: k(ε/2k) = ε/2 (I coudldn't find the correct font for ε here, so I used ε instead of the one in the book. I was accused of dishonesty in the past for doing this, so I'm getting that out of the way now)The Everything Guide to Algebra: Christopher MonahanDescribes "PEMDAS" in detail, then later, on page 46 shows: 6x³÷3x=2x²(That's because "3x" is a single quantity/operand, and is a product of both factors: 3 and x)Basic Algebra I: Second Edition By Nathan Jacobsonhttps://books.google.ca/books?id=JHFpv0tKiBAC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=falsepg 116: a/b + c/d = (ad +bc)/bdIntroduction to Algebra By Peter Jephson Cameronhttps://books.google.ca/books?id=syYYl-NVM5IC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q=mx&f=falsePage 17 "Since mx/nx = m/n" [Notice how it is NOT m * x / n * x = mx²/n ???]FACTORS and COEFFICIENTS:https://books.google.ca/books?id=yRRtCgAAQBAJ&printsec=frontcover#v=onepage&q&f=falseOther links:http://www.onlinemathlearning.com/multiply-divide-expressions.htmlhttp://www.purplemath.com/modules/orderops2.htm (Elizabeth Stapel: http://www.purplemath.com/resume.htm)Discussion on algebra: http://www.jstor.org/stable/pdf/2972726.pdf→So now I have made my long winded point that 8 ÷ 2x = 4/x, replace 'x' with 3+1 and we have precisely:8 ÷ 2x = 4/x8 ÷ 2(3+1) = 4/(3+1)8 ÷ 2(4) = 4/(4)1 = 1→I believe that 20 years ago this would have been a non-argument, but since the emergence of calculators, math websites, and computers, a particular convention must be chosen for the programming of such calculating devices, alleviating the student of actual understanding of how things are performed. Even Wolfram|Alpha has used both conventions over the last few years, changing 8 ÷ 2x = 4/n to 8 ÷ 2x = 4x. In this case, the user, being a good student and knowledgeable to basic math, realizes what is going on and must use a bunch of parenthesis that would not be required on paper: 8 ÷ (2x). Just as some math books declare their conventions, so do calculators, stating something like "implicit multiplication will not be given precedence in the order of operations" meaning 8 ÷ 2x ≠ 8 ÷ (2x). This is for ease of programming since programmers cannot easily program a human's understanding of notation. The code must be very rigid.→So, in summary, in order to obey all the principles at the same time, 8 ÷ 2(3+1) = 1, otherwise, you run into the issue that 8 ÷ 2x = 4x, which would cause thousands of mathematicians to roll over in their graves, those who founded the very concepts of algebra.→I welcome comments backed up with mathematical references, just as I have done. Thanks for reading and please share if you see anymore of these trolling equations pop up on social media, youtube, or similar.EDIT: ab = ba8 ÷2a = 8 ÷ a2Let a = 4I'll leave the rest to you.EDIT: Bruce Alan Martin has disabled comments on his programming language answer, thus computer programmers and engineers are not able to challenge his response. The issue for the original question is not one of computer language, but rather a mathematical one. Computer programmers need to use mathematics and conventions in their code so stating "language A does it this way" is not any authority for the actual mathematics.

First impressions matter - especially on the first day of class. Students arrive with a mix of emotions. Most, however, are nervous. The reasons vary from child to child, but kids tend to feel anxious about starting something new. This is not necessarily a bad thing; some anxiety is normal, even healthy. However, teachers can do a lot to ensure their classrooms are safe and welcoming on the first day of online classes. Those are:#1 Use Video to Welcome Students to Your Online CourseCourse welcome videos are great for keeping your students engaged and opening up the dialogue between you and your students. According to many educational experts, nothing will catch your students' attention like a great welcome video. It’s a great way to say hello, introduce yourself, and let students know what they can expect.Your welcome video should achieve the following objectives:Help students become familiar with both you and the course.Ease any anxiety about taking an online course.Show students you are accessible and approachable.Set the stage for continued, positive interactions between you and the student.#2 Welcome Students to Your Online Course with a Welcome LetterNot everyone is going to want to watch your course introduction welcome video, so we suggest creating a welcome letter, too. Keep in mind this should not be a transcript of your welcome video. It’s simply another way students can digest the information you’ve included in your video.The outline of your welcome letter should look like this:Greeting/Introduction – Welcome your students and tell them a little bit about yourself.How to Access the Course – Include information about the Learning Management System and how to access it.Support – List your office hours and ways your students can get in touch with you (email address, phone number, etc.).Be sure to keep your tone light and friendly. Remember, people read text in a negative tone more often than in a positive one.#3 Welcome Students By Offering Online Office HoursOne of the most attractive qualities in a traditional educational environment is the constant one-on-one communication. Your online students need to know that when they reach out to you, you’ll be able to answer them in a timely manner. Many experts points out that the role of the instructor is critical in pushing students to excel and engage in material. That’s you!I would suggest welcoming students with information about your availability hours. Try offering them at least twice a week if you can.Here are a few ways you can offer to communicate with your students during office hours:EmailOnline Discussion ForumPhone CallsVideo Messaging#4 Welcome Students with an Online Discussion ForumAn online discussion forum is a great way for students to interact with you and with each other. Research suggests that an introduction forum is the best way to get the ball rolling.Start the forum by introducing yourself and encouraging others to do the same. Point out that the purpose of the discussion forum is to meet other students enrolled in the course, so they know they’re not alone.Thanks for giving me the opportunity to answer this question. I hope you find my answer helpful.Do upvote my answer and follow my handle for more informative answers.

My 1st Day at NIT-Raipur3rd August 20171st Class - ChemistryScheduled Time for 1st Class was 9.15 am, since we were new to this College, most of us were wondering where our classrooms are?Each floor looked same, I asked the Guard standing at Entry Gate where the Room SN-2 is? He told and I followed the Way. I reached the Room in 5 minutes, door was closed and 2 students were standing exactly in front of the Door. I asked them, ‘IT Branch'? They said Yes, then I entered the Room with both of them. All 3 of us sat on the same bench and started waiting for the Teacher to come.Teacher arrived, gave his Introduction, welcomed all of us, Congratulated us for making it to NIT. And since it was the 1st class he told a story instead of teaching Chemistry.2nd Class - MathsA Ma'am came, and similarly welcomed and congratulated us. She told the Basics of Complex Number and class over.3rd Class - PhysicsSame followed. The Teacher told us about the Division of Batches into two groups for Practical Sessions (since our strength is 91 whole batch is divided into 2 Sub-Batches for convenience of Practicals)4th Class - Basic Electrical EnggA Bengali Ma'am came and immediately started teaching like Hell.Lunch BreakI got to my Hostel, ate, relaxed for a while then got ready for 2nd Half.5th Class - BEE LabIt was BEE Lab for students whose name starts with letter A to M and Mechanics Lab for students having name starting from letter N to Z. We tried to find the Lab for 10 minutes and then a Teacher himself took us into the Lab. A Sardar came in the traditional Punjabi dress, he introduced himself and so welcomed us into NIT. He told the list of Experiments that we will be performing in this semester. Class Over.6th Class - LanguageWe waited in the Room for about half and hour, no one came and so we left.Overall my 1st Day at College was just like any random day at College. Our Orientation program took months after our Classes had started. I still do not remember the 2nd Person whom I met on the Classroom Door on the 1st Day (Though I remember the 1st one). Some of my Classmates are active on Quora and they can easily relate our 1st Day at NIT-Raipur.